Instants in physics - point mechanics and general relativity

TL;DR

This paper explores the concept of 'instants' in physics, comparing their roles in point mechanics and general relativity, and discusses foundational issues related to relationalism and the nature of time.

Contribution

It provides a comparative analysis of the notion of 'instant' in point mechanics and general relativity, highlighting overlooked aspects in modern dynamics and foundational differences.

Findings

Relational point mechanics can determine durations from 'instants'

The notion of 'instant' is less straightforward in general relativity

Foundational differences exist between relationalism in mechanics and field theory

Abstract

Theories in physics usually do not address ``the present''or ``the now''. However, they usually have a precise notion of an ``instant'' (or state). I review how this notion appears in relational point mechanics and how it suffices to determine durations - a fact that is often ignored in modern presentations of analytical dynamics. An analogous discussion is attempted for General Relativity. Finally I critically remark on the difference between relationalism in point mechanics and field theory and the problematic foundational dependencies between fields and spacetime.